Determination of the truncation order and numerical window for modeling general dielectric waveguides by the Fourier method

Ramanujam, N.; Li, Lifeng; Burke, James J.; Gribbons, M.

doi:10.1109/50.485613

Cited by 9 publications

(9 citation statements)

References 12 publications

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“…In this paper, we adopt techniques from Tang [22] and Ramanujam et al [23] and combine them to offer a new novel approach for determining for HG and LG. In [22], Tang proposed an interesting and definite procedure to choose for Gaussian-type functions that is expanded by the first 1 HG of order using the expression of series coefficients as given by (9) in spectral space.…”

Section: Choice Of Scaling Factormentioning

confidence: 99%

“…In contrast to HG or LG, can be independently accommodated in each outer region. We write (23) where , , are the grid point values as in (10). At each collocation point , we obtain (24) which is equivalent to (25) For the HG basis functions, are the zeros of with the order , while for LG, are the zeros of plus .…”

Section: Choice Of Scaling Factormentioning

confidence: 99%

“…The finite support in Tang's work was assumed to be given by a simple truncation of infinite domain into a finite support. In [23], a novel technique has been proposed in Galerkin method with trigonometric basis functions (the Fourier method) for the a-priori determination of the finite support (or numerical window in [23]) of the Fourier method by using the Wentzel-Kramers-Brillouin (WKB) method and effective index method (EIM). Here we adopt this technique to determine for in (27) in our SCM with DD.…”

Section: Choice Of Scaling Factormentioning

confidence: 99%

“…Once we have obtained , can be determined by (33) and is calculated through . Using the same definition as [23], we denote the decay rates for the mode as…”

Section: Choice Of Scaling Factormentioning

confidence: 99%

“…Contrarily, the large ratio represents the field strength at may not be negligible. In this paper, following Ramanujam et al [23], we take the ratio as 0.01. Hence, to find the finite support in each direction, we first let…”

Section: Choice Of Scaling Factormentioning

confidence: 99%

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An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition

Huang

Yang²

2003

J. Lightwave Technol.

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An accurate and efficient solution method using spectral collocation method with domain decomposition is proposed for computing optical waveguides with discontinuous refractive index profiles. The use of domain decomposition divides the usual single domain into a few subdomains at the interfaces of discontinuous refractive index profiles. Each subdomain can be expanded by a suitable set of orthogonal basis functions and patched at these interfaces by matching the physical boundary conditions. In addition, a new technique incorporating the effective index method and the Wentzel-Kramers-Brillouin method for the a-priori determination of the scaling factor in Hermite-Gauss or Laguerre-Gauss basis functions is introduced to considerably save computational time without experimenting with it. This method shares the same desirable property of the spectral collocation method of providing a fast and accurate solution but avoids the oscillatory solutions and improves the poor convergence problem of the simple spectral collocation method with single domain where regions of discontinuous refractive index profiles exist. Applications to several two-and three-dimensional waveguide structures having exact or accurate approximate solutions are given to test the accuracy and efficiency; all the results are found to be in excellent agreement. Index Terms-Discontinuous refractive index profiles, domain decomposition, optical waveguides, orthogonal basis function, scaling factor, spectral collocation method. I. INTRODUCTION R ECENTLY, there has been growing interest in developing integrated optics devices in optical communication systems. The fundamental operating principle and optimal design of optical devices such as modulators, switches, filters, fibers, and semiconductor lasers are often based on the comprehension of optical waveguide theory [1]. Hence, solving the optical waveguide problems is an essential way to clearly realize these devices. However, only a limited number of waveguides, which have simple geometry and specific refractive index profiles (RIPs), have analytic solutions [1], [2]. Consequently, employing

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Section: Choice Of Scaling Factormentioning

confidence: 99%

Section: Choice Of Scaling Factormentioning

confidence: 99%

Section: Choice Of Scaling Factormentioning

confidence: 99%

“…Once we have obtained , can be determined by (33) and is calculated through . Using the same definition as [23], we denote the decay rates for the mode as…”

Section: Choice Of Scaling Factormentioning

confidence: 99%

Section: Choice Of Scaling Factormentioning

confidence: 99%

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